Final answer:
The Lerner Index for a monopoly can be calculated with the formula (Price - Marginal Cost) / Price, using the monopoly's charge price and marginal cost. However, the exact Lerner Index cannot be calculated without the monopolist's marginal revenue and actual quantity produced, which are not provided.
Step-by-step explanation:
To calculate the Lerner Index for a monopoly, we use the formula (Price - Marginal Cost) / Price. Given the inverse demand function P = 40 - 1.5Q and the inverse supply function for marginal cost P = 4 + 1.5Q, we first find the quantity supplied by the monopoly where marginal revenue equals marginal cost. Unfortunately, without the marginal revenue curve, this cannot be done directly from the given functions.
However, if we proceed under the assumption that the monopoly is maximizing profit, we can derive the marginal revenue curve from the demand function (which is P = 40 - 1.5Q for the corresponding quantity). Once we have the quantity where MR=MC, we can solve for the price the monopoly charges from the demand curve and the marginal cost from the supply curve.
Then, assuming the quantity that the monopoly decides to produce and sell (Qm) is found where marginal revenue equals marginal cost, the Lerner Index would involve plugging this quantity into the inverse demand and supply functions to get the monopoly charge price (P) and the marginal cost (MC) respectively. Once P and MC are known, the Lerner Index can be computed as (P - MC) / P.
Please note that due to information constraints regarding the monopolist's marginal revenue and actual quantity produced, an exact numerical answer cannot be provided without additional data.